




"""simple docstring"""

from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean




def     _A					( __lowercase    ):





       """simple docstring"""



       def is_in_circle(__lowercase							,     __lowercase    ) -> bool:
              lowerCamelCase__          =						sqrt((x**2) + (y**2)    )
              # Our circle has a radius of 1, so a distance
              # greater than 1 would land outside the circle.
              return distance_from_centre <= 1

       # The proportion of guesses that landed in the circle
       lowerCamelCase__          =						mean(
           int(is_in_circle(uniform(-1.0							,     1.0    )							,     uniform(-1.0							,     1.0    )    )    )
           for _ in range(a__    )    )
       # The ratio of the area for circle to square is pi/4.
       lowerCamelCase__          =						proportion * 4
       print(f"""The estimated value of pi is {pi_estimate}"""    )
       print(f"""The numpy value of pi is {pi}"""    )
       print(f"""The total error is {abs(pi - pi_estimate    )}"""    )




def     _A					( __lowercase							,     __lowercase							,     __lowercase = 0.0							,     __lowercase = 1.0							,     ):





       """simple docstring"""



       return mean(
           function_to_integrate(uniform(a__							,     a__    )    ) for _ in range(a__    )    ) * (max_value - min_value)




def     _A					( __lowercase							,     __lowercase = 0.0							,     __lowercase = 1.0    ):





       """simple docstring"""



       def identity_function(__lowercase    ) -> float:
              return x

       lowerCamelCase__          =						area_under_curve_estimator(
           a__							,     a__							,     a__							,     a__    )
       lowerCamelCase__          =						(max_value * max_value - min_value * min_value) / 2

       print("""******************"""    )
       print(f"""Estimating area under y=x where x varies from {min_value} to {max_value}"""    )
       print(f"""Estimated value is {estimated_value}"""    )
       print(f"""Expected value is {expected_value}"""    )
       print(f"""Total error is {abs(estimated_value - expected_value    )}"""    )
       print("""******************"""    )




def     _A					( __lowercase    ):





       """simple docstring"""



       def function_to_integrate(__lowercase    ) -> float:
              return sqrt(4.0 - x * x    )

       lowerCamelCase__          =						area_under_curve_estimator(
           a__							,     a__							,     0.0							,     2.0    )

       print("""******************"""    )
       print("""Estimating pi using area_under_curve_estimator"""    )
       print(f"""Estimated value is {estimated_value}"""    )
       print(f"""Expected value is {pi}"""    )
       print(f"""Total error is {abs(estimated_value - pi    )}"""    )
       print("""******************"""    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()














"""simple docstring"""


# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput




class 						__UpperCamelCase     (     UpperCamelCase						):
					def __init__(							self							:	str     , UpperCAmelCase							:	Union[str, Any]     , UpperCAmelCase							:	str   )	->       Any:
											super().__init__()
											self.register_modules(unet=UpperCAmelCase     , scheduler=UpperCAmelCase   )
					@torch.no_grad()
					def __call__(							self							:	int     , UpperCAmelCase							:	int = 1     , UpperCAmelCase							:	Optional[torch.Generator] = None     , UpperCAmelCase							:	int = 50     , UpperCAmelCase							:	Optional[str] = "pil"     , UpperCAmelCase							:	bool = True     , **UpperCAmelCase							:	Dict     , )	->       Union[ImagePipelineOutput, Tuple]:
											lowerCAmelCase   :Optional[Any]						=			torch.randn(
											    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)     , generator=UpperCAmelCase     , )
											lowerCAmelCase   :str						=			image.to(self.device   )

											# set step values
											self.scheduler.set_timesteps(UpperCAmelCase   )

											for t in self.progress_bar(self.scheduler.timesteps   ):
																	# 1. predict noise model_output
																	lowerCAmelCase   :Dict						=			self.unet(UpperCAmelCase     , UpperCAmelCase   ).sample

																	# 2. predict previous mean of image x_t-1 and add variance depending on eta
																	# eta corresponds to η in paper and should be between [0, 1]
																	# do x_t -> x_t-1
																	lowerCAmelCase   :List[str]						=			self.scheduler.step(UpperCAmelCase     , UpperCAmelCase     , UpperCAmelCase   ).prev_sample

											lowerCAmelCase   :Any						=			(image / 2 + 0.5).clamp(0     , 1   )
											lowerCAmelCase   :Tuple						=			image.cpu().permute(0     , 2     , 3     , 1   ).numpy()
											if output_type == "pil":
																	lowerCAmelCase   :Dict						=			self.numpy_to_pil(UpperCAmelCase   )

											if not return_dict:
																	return (image,), "This is a local test"

											return ImagePipelineOutput(images=UpperCAmelCase   ), "This is a local test"